In this article the author considers problems of the relations, interaction, and mutual transitions of the function of prosecution under criminal investigation. Criminal prosecution was not procedurally established previously in the implementation of UPK RT (1961). Instead, the procedure for the initiation of a criminal case was fixed. From the fact that this is new, it is possible to assume that, since April 1, 2010, its application will cause problems. Firstly, it is caused by an outdated legal base in this area, and secondly, a deficiency in the methodical maintenance by law enforcement bodies to investigate criminal cases of the private, private-public and public prosecution. The urgency of the chosen topic is not in question, as it is, in turn starting with UUS 1864, and currently doesn't cease to be controversial, both in theory and practice of the application of legislation of the legal institutes. Thus, various opinions, statements of outstanding eminent scientists on the above issues, their analysis, processing, and corresponding conclusions are considered. In passing, also considered is the question on a parity of criminal prosecution, implementation of the criminal case and implementation of the criminal prosecution, and debate about the conclusions, the analysis of the insights of practitioners, statistics and a number of other questions connected with this topic, and also extensive analysis and consideration of the legal literature taking into account the historical and legal analysis. (Published Abstract)